NEET Atoms and Nuclei — Set 3

Question 1

What does de Broglie’s hypothesis explain in the context of Bohr’s model?

Accepted Answer

De Broglie’s hypothesis explains the quantization of angular momentum by proposing that electrons form standing waves, with the orbit circumference being an integral multiple of the wavelength.

Question 2

An alpha-particle with kinetic energy 6.0 MeV approaches a gold nucleus (Z = 79). What is the distance of closest approach? (Use $ \frac{1}{4\pi\epsilon_0} = 9 \times 10^9 \, \text{N·m}^2/\text{C}^2 $, $ e = 1.6 \times 10^{-19} \, \text{C} $, 1 MeV = $ 1.6 \times 10^{-13} \, \text{J} $)

Accepted Answer

$ d = \frac{2Ze^2}{4\pi\epsilon_0 K} $. $ K = 6.0 \times 1.6 \times 10^{-13} = 9.6 \times 10^{-13} \, \text{J} $. $ d = \frac{2 \times 79 \times (1.6 \times 10^{-19})^2 \times 9 \times 10^9}{9.6 \times 10^{-13}} $. $ d = \frac{3.641 \times 10^{-28}}{9.6 \times 10^{-13}} \approx 3.79 \times 10^{-14} \, \text{m} \approx 38 \, \text{fm} $.

Question 3

A hydrogen atom absorbs a photon of energy 1.89 eV from the $ n = 2 $ state. To which energy level does it jump? (Use $ E_n = -\frac{13.6}{n^2} \, \text{eV} $)

Accepted Answer

$ E_2 = -3.4 \, \text{eV} $. $ E_n = -3.4 + 1.89 = -1.51 \, \text{eV} $. $ -1.51 = -\frac{13.6}{n^2} \Rightarrow n^2 = 9 \Rightarrow n = 3 $.

NEET Physics: Atoms and Nuclei — Practice Set 3

Q1. What does de Broglie’s hypothesis explain in the context of Bohr’s model?

Q2. An alpha-particle with kinetic energy 6.0 MeV approaches a gold nucleus (Z = 79). What is the distance of closest approach? (Use \( \frac{1}{4\pi\epsilon_0} = 9 \times 10^9 \, \text{N·m}^2/\text{C}^2 \), \( e = 1.6 \times 10^{-19} \, \text{C} \), 1 MeV = \( 1.6 \times 10^{-13} \, \text{J} \))

Q3. A hydrogen atom absorbs a photon of energy 1.89 eV from the \( n = 2 \) state. To which energy level does it jump? (Use \( E_n = -\frac{13.6}{n^2} \, \text{eV} \))

Q4. A 13.0 eV electron beam excites a hydrogen atom in the ground state. What is the highest energy level reached? (Use \( E_n = -\frac{13.6}{n^2} \, \text{eV} \))

Q5. In Bohr’s model, what is the physical basis for the quantization of angular momentum?

Q6. Why does the classical electromagnetic theory predict that an atom should collapse?

Q7. According to Bohr’s model, what happens when an electron in a hydrogen atom transitions from a higher orbit to a lower orbit?

Q8. A hydrogen atom absorbs a photon of energy 12.75 eV from the ground state. To which energy level does it jump? (Use \( E_n = -\frac{13.6}{n^2} \, \text{eV} \))

Q9. An alpha-particle with 4.0 MeV kinetic energy approaches a gold nucleus (Z = 79). What is the distance of closest approach? (Use \( \frac{1}{4\pi\epsilon_0} = 9 \times 10^9 \, \text{N·m}^2/\text{C}^2 \), \( e = 1.6 \times 10^{-19} \, \text{C} \), 1 MeV = \( 1.6 \times 10^{-13} \, \text{J} \))

Q10. According to Thomson’s model of the atom, how is the positive charge distributed?